7 papers
Metrizability of Mahavier products indexed by partial orders
Steven Clontz, Jacob Dunham
Let be separable metrizable, and let be a non-trivial relation on . For a given partial order , the Mahavier product (also…
Arhangelskii's -principles and selection games
Steven Clontz
Arhangelskii's properties and defined for convergent sequences may be characterized in terms of Scheeper's selection principles. We generalize these results to hold for…
On Ramsey properties, function spaces, and topological games
Steven Clontz, Alexander V. Osipov
An open question of Gruenhage asks if all strategically selectively separable spaces are Markov selectively separable, a game-theoretic statement known to hold for countable spaces…
Dual Selection Games
Steven Clontz
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strateg…
Limited Information Strategies and Discrete Selectivity
Steven Clontz, Jared Holshouser
We relate the property of discrete selectivity and its corresponding game, both recently introduced by V.V. Tkachuck, to a variety of selection principles and point picking games.…
Mahavier Products, Idempotent Relations, and Condition
Steven Clontz, Scott Varagona
Clearly, a generalized inverse limit of metrizable spaces indexed by is metrizable, as it is a subspace of a countable product of metrizable spaces. The authors previou…